| There are two parts in the thesis. The first part deals with the problem of global stabilization of linear systems with bounded feedback. A linear system can be globally stabilized by a bounded feedback if and only if all eigenvalues of the system matrix have nonpositive real parts and all eigenvalues of the uncontrollable part have strictly negative real parts. If a linear system satisfies this condition, then we can provide an algorithm to find a bounded stabilizing feedback. The design employs linear combinations and compositions of linear functions and saturations. We also show that if we use only a saturated linear feedback, then a linear system cannot be globally stabilized in general. Some applications, such as output feedback stabilization, the stabilization of cascade systems, and the stabilization of flight control, are also presented here.;The second part deals with questions of global stabilizability of nonlinear systems. Based on the use of control-Lyapunov functions, we obtain a class of stabilizing feedback laws. A sufficient condition for such feedbacks to be continuously differentiable is presented. We then apply this condition to a wide class of two- and three-dimensional systems, extending some recent results on stabilization. |
